Tsallis Maximum Entropy Lorenz Curves
Authors
Abstract:
In this paper, at first we derive a family of maximum Tsallis entropy distributions under optional side conditions on the mean income and the Gini index. Furthermore, corresponding with these distributions a family of Lorenz curves compatible with the optional side conditions is generated. Meanwhile, we show that our results reduce to Shannon entropy as $beta$ tends to one. Finally, by using actual data, we compare the maximum Tsallis entropy Lorenz curve with some parametric Lorenz curves.
similar resources
Tissue radiation response with maximum Tsallis entropy.
The expression of survival factors for radiation damaged cells is currently based on probabilistic assumptions and experimentally fitted for each tumor, radiation, and conditions. Here, we show how the simplest of these radiobiological models can be derived from the maximum entropy principle of the classical Boltzmann-Gibbs expression. We extend this derivation using the Tsallis entropy and a c...
full textTsallis Entropy and Conditional Tsallis Entropy of Fuzzy Partitions
The purpose of this study is to define the concepts of Tsallis entropy and conditional Tsallis entropy of fuzzy partitions and to obtain some results concerning this kind entropy. We show that the Tsallis entropy of fuzzy partitions has the subadditivity and concavity properties. We study this information measure under the refinement and zero mode subset relations. We check the chain rules for ...
full textProjective Power Entropy and Maximum Tsallis Entropy Distributions
We discuss a one-parameter family of generalized cross entropy between two distributions with the power index, called the projective power entropy. The cross entropy is essentially reduced to the Tsallis entropy if two distributions are taken to be equal. Statistical and probabilistic properties associated with the projective power entropy are extensively investigated including a characterizati...
full textOn Tsallis Entropy Bias and Generalized Maximum Entropy Models
In density estimation task, maximum entropy model (Maxent) can effectively use reliable prior information via certain constraints, i.e., linear constraints without empirical parameters. However, reliable prior information is often insufficient, and the selection of uncertain constraints becomes necessary but poses considerable implementation complexity. Improper setting of uncertain constraints...
full textQualms concerning Tsallis’ Use of the Maximum Entropy Formalism
Tsallis’ ‘statistical thermodynamic’ formulation of the nonadditive entropy of degree-α is neither correct nor self-consistent. It is well known that the maximum entropy formalism [1], the minimum discrimination information [2], and Gauss’ principle [3, 4] all lead to the same results when a certain condition on the prior probability distribution is imposed [5]. All these methods lead to the sa...
full textAn Efficient Algorithm for Maximum Tsallis Entropy using Fenchel-duality
We derive a dual-primal recursive algorithm based on the Fenchel duality framework, extending Dykstra’s successive projections and Csiszar’s I-projections schemes, to handle Tsallis MaxEnt. The Tsallis entropy Sq(p) is a one-parameter extension of Shannon’s entropyH(p) in the sense that Sq→1(p) = H(p). The solution of the Tsallis MaxEnt falls under a q-deformed Gibbs distribution which is a pow...
full textMy Resources
Journal title
volume 11 issue 1
pages 41- 56
publication date 2014-09
By following a journal you will be notified via email when a new issue of this journal is published.
Hosted on Doprax cloud platform doprax.com
copyright © 2015-2023